Optimal immunity control and final size minimization by social distancing for the SIR epidemic model
This paper studies optimal immunity control and final size minimization by social distancing for the SIR epidemic model. The herd immunity is described by the value of susceptible population \(S\) below which the number of infected decreases and is defined as \(R_0^{-1}\). The paper focuses on the optimal control issue of obtaining the largest value for the limit number of susceptible population at infinity \(S_{\infty}\) by enforcing social distancing. It determines how close to the herd immunity threshold it is possible to stop the spread of a disease. In this case, no vaccine or treatment is found to modify the evolution of the disease. The study is mainly based on the consideration of using partial lockdown, where interventions take place only on a finite time interval. The existence and uniqueness of the solution to the optimal control problem are established. It is bang-bang with a unique commutation from the nominal value to the minimum transmission rate. Some numerical simulations have also been performed.
scientific article; zbMATH DE number 7359208
scientific article